Complete Resolution of the "True Nature of Dark Energy" and the "Hubble Tension" Based on Discrete Topological Geometry: From the Microscopic Information Structure of the Multiplication Table to the Emergence of a "1:4 Hyperelliptical Universe"

This paper proposes a novel cosmological model that completely resolves the greatest outstanding issues in modern cosmology: the "true nature of dark energy" and the "Hubble tension," utilizing a single algorithm based on discrete topological geometry. Building upon the interference of spin phases derived from elementary arithmetic "modulo operations" (the multiplication table) and the "1/2 critical line," we extend the "1:4 packing limit" required by the stability of quantum information to a macroscopic 4D spacetime metric. We demonstrate the mechanism by which, when the information density relative to the volume of the universe reaches the holographic bound (at a redshift of ), spacetime exhibits "geometric rigidity," refusing further information densification. This acts as an effective cosmological constant (repulsive force) and drives accelerated expansion. Furthermore, by calculating the geometric distortion of geodesics in this 1:4 hyperelliptical metric, we show that the observational discrepancy in the Hubble constant between the early universe (CMB) and the local universe (supernovae) is fully integrated without the need for additional physical constants. This study is an attempt to uniformly describe everything from microscopic quantum phases to macroscopic cosmological expansion dynamics as the "geometry of information."